The Weibull-power cauchy distribution: Model, properties and applications

M. H. Tahir, M. Zubair, Gauss M. Cordeiro, Ayman Alzaatreh, M. Mansoor

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We propose a new three-parameter distribution with increasing, decreasing, reversed-J and upside-down bathtub shaped hazard rate, called the Weibull-power Cauchy distribution. We obtain explicit expressions for the mode, ordinary, negative and incomplete moments, mean deviations, mean residual life, quantile and generating functions, order statistics, Shannon entropy and reliability. We derive a power series for the quantile function using exponential partial Bell polynomials. A useful characterization of the new distribution is also presented. The method of maximum likelihood is used to estimate the model parameters. The importance of the new distribution is proved empirically by means of three real-life data sets.

Original languageEnglish
JournalHacettepe Journal of Mathematics and Statistics
Issue number4
Publication statusPublished - 2017


  • Cauchy distribution
  • Half-Cauchy distribution
  • Moments
  • Power Cauchy distribution
  • T-X family
  • Weibull-X family

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Geometry and Topology

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